OPENING QUESTIONS:
Radial acceleration takes into account that angular velocity may be increasing or decreasing AND/OR radius may be changing.
In either of those situations, the resulting vector does not necessarily point towards the center of the circle.
We will ALMOST always work with the situation where angular velocity is constant AND the radius is constant... therefore in those instances, the centripetal acceleration is the same as the radial acceleration!
See if you can make THAT make sense vis-a-vis our homework
OBJECTIVE:
I will be able to solve basic circular motion problems during today's class.
WORDS FOR TODAY:
- centrifugal motion (inaccurate)
- centripetal motion (center-seeking)
- period (time for one revolution)
- angular velocity = ω = radians/sec
- linear velocity = rω =(meters)(rad)/(sec) = m/sec
- angular acceleration = α = radians/sec2
- linear acceleration = rω2 = (meters)(rad2)/(sec2) = m/sec2
FORMULAE OBECTUS:
centripetal acceleration:
ac = v2/r
period:
T = 2πr/v
angular speed:
ω=2π/T (radians/sec)
tangential velocity:
v = rω (meters/sec)
tangential acceleration:
a = rω2 (meters/sec2) = rα
WORK O' THE DAY:
Let's talk extra practice:
MC once/twice a week? FR once per week?
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Let's take a gander at the Homework:
Review these in terms of our opening question: 40 & 41
Be prepared to explain THIS:
Worked example 6.5 on page 155 The book leaves a particularly important concept left out in that example... what would that be?
Fun with 2001. Taking whatever data you are able, please suggest a SIZE for the space station shown during this clip (I'll leave it to you, my MOST gracious and humble students to determine an appropriate definition for that in this context). 1 (and only ONE) hint is available. But all you really need to know is shown in that video and on our formulae objectus above.
Now let's get a GENERAL idea of the volume of the exterior of that space station by googling the surface area of a cyliner HERE.
If time permits... work with your group to ESTIMATE the cost of all that steel if it is 1.0 centimeter thick (that's probably a high estimate, so feel free to adjust)
HW Probs:
Conceptual Problem #6 on page 168, Problems 2, 3, 4 and 7 on page 169. Also, let's turn back to chapter 4 and do #39....
If you're up for a nasty challenge, try researching the diff eq 6.5 (what happens when we DO NOT ignore air friction) on page 163 (we will NOT cover this in class, but I'd love to see what you come up with)